高一数学三角恒等变题..
问题描述：
高一数学三角恒等变题..
1 cos36°cos72°=?
2 sin10°sin30°sin50°sin70°=?
答
1 cos36°cos72°
=2sin36cos36°cos72°/2sin36
=sin72cos72/2sin36
=sin144/4sin36
=sin36/4sin36
=1/4
2 sin10°sin30°sin50°sin70°
=cos80cos60cos40cos20
=1/2cos20cos40cos80
=2sin20cos20cos40cos80/4sin20
=sin40cos40cos80/4sin20
=sin80cos80/8sin20
=sin160/16sin20
=sin20/16sin20
=1/16为什么..... sin144/4sin36 =sin36/4sin36 sin144是怎么换算成sin36的呢?sin144=sin(180-144)=sin36